1742, present participle adjective from bask (v.). Basking shark is recorded from 1769.

bask

v.

late 14c., basken "to wallow (in blood)," with loss of middle syllable, from Old Norse baðask "to bathe oneself," reflexive of baða "bathe" (see bathe). Modern meaning "soak up a flood of warmth" is apparently due to Shakespeare's use of the word in reference to sunshine in "As You Like It" (1600). Related: Basked; basking.